II. I summed up Coase's analysis as consisting of three parts: Nothing works. Everything works. It all depends (on transaction costs). Pick one of the three, and explain that part of the argument in your own words.
1: Nothing Works. This is Coase's critique of Pigou: An externality is typically a cost that results from decisions by both parties--A's decision to play loud music plus his roommate B's decision to try to sleep or study at the same time. We do not, in the general case, know which party can eliminate the cost more easily--and the best solution might involve adjustment by both parties--A can play loud music except during exam week. So a legal rule of the sort proposed by Pigou, which makes one party liable (to the other or to the state) for the cost, will only give the right result if the best solution happens to consist of only that party adjusting.
2. Everything Works (aka the Coase Theorem): In a world of zero transaction costs, any initial assignment of rights will lead to an efficient outcome. The reason is that if the outcome were inefficient, there would be some bargain to change it that would benefit all concerned--and in a world of zero transaction costs, such a bargain will get made.
3. It All Depends (on transaction costs): Getting from some initial assignments of rights (for example, the factory may pollute the lake) to some final outcomes (for example, the factory stops polluting) requires a transaction (the resort owners pay the factory to stop polluting). Such transactions may be costly--in the example, if there are many resort owners they face a public good problem in organizing to pay the factory to stop polluting. So in choosing an initial assignment, one should consider not only how likely it is to lead directly to the efficient outcome (in the example, if the efficient outcome were for the factory to pollute and the resorts to adjust) but also how hard it will be to get to other outcomes (no pollution, for example) if they turn out to be the efficient ones, and how likely that is.